Linear photonic processors and related methods

ABSTRACT

Photonic processors are described. The photonic processors described herein are configured to perform matrix-matrix (e.g., matrix-vector) multiplication. Some embodiments relate to photonic processors arranged according to a dual-rail architecture, in which numeric values are encoded in the difference between a pair optical signals (e.g., in the difference between the powers of the optical signals). Relative to other architectures, these photonic processors exhibit increased immunity to noise. Some embodiments relate to photonic processors including modulatable detector-based multipliers. Modulatable detectors are detectors designed so that the photocurrent can be modulated according to an electrical control signal. Photonic processors designed using modulatable detector-based multipliers are significantly more compact than other types of photonic processors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation claiming the benefit under 35 U.S.C.§ 120 of U.S. application Ser. No. 17/398,384, filed Aug. 10, 2021,under Attorney Docket No. L0858.70023US03, entitled “LINEAR PHOTONICPROCESSORS AND RELATED METHODS,” which is hereby incorporated herein byreference in its entirety.

U.S. application Ser. No. 17/398,384 is a Division claiming the benefitunder 35 U.S.C. § 120 of U.S. application Ser. No. 17/101,415, filedNov. 23, 2020, under Attorney Docket No. L0858.70023US02, entitled“LINEAR PHOTONIC PROCESSORS AND RELATED METHODS,” which is herebyincorporated herein by reference in its entirety.

U.S. application Ser. No. 17/101,415 claims the benefit under 35 U.S.C.§ 119(e) of U.S. Provisional Patent Application Ser. No. 62/939,480,entitled “SYSTEMS AND METHODS FOR ANALOG COMPUTING,” filed on Nov. 22,2019 under Attorney Docket No. L0858.70016US01, U.S. Provisional PatentApplication Ser. No. 62/962,759, entitled “MODULATABLE DETECTOR-BASEDMULTIPLIERS,” filed on Jan. 17, 2020 under Attorney Docket No.L0858.70023US00, U.S. Provisional Patent Application Ser. No.62/963,315, entitled “DUAL-RAIL PHOTONIC MULTIPLIER SYSTEM WITHAPPLICATIONS TO LINEAR PHOTONIC PROCESSOR,” filed on Jan. 20, 2020 underAttorney Docket No. L0858.70022US00, U.S. Provisional Patent ApplicationSer. No. 62/970,360, entitled “MODULATABLE DETECTORS,” filed on Feb. 5,2020 under Attorney Docket No. L0858.70026US00, and U.S. ProvisionalPatent Application Ser. No. 62/978,181, entitled “MODULATABLEDETECTORS,” filed on Feb. 18, 2020 under Attorney Docket No.L0858.70026US01, each of which is hereby incorporated herein byreference in its entirety.

BACKGROUND

Deep learning, machine learning, latent-variable models, neural networksand other matrix-based differentiable programs are used to solve avariety of problems, including natural language processing and objectrecognition in images. Solving these problems with deep neural networkstypically requires long processing times to perform the requiredcomputation. The most computationally intensive operations in solvingthese problems are often mathematical matrix operations, such as matrixmultiplication.

SUMMARY OF THE DISCLOSURE

Some embodiments relate to a method for performing a mathematicaloperation comprising: receiving an input optical signal; obtaining afirst numeric value and a second numeric value; generating first andsecond encoded optical signals by modifying the input optical signalusing the first numeric value; generating first and second encodedoutput signals using the second numeric value and the first and secondencoded optical signals; and obtaining a result of the mathematicaloperation using the first and second encoded output signals.

In some embodiments, the first and second encoded output signals areoptical signals.

In some embodiments, a difference between the first and second encodedoutput signals is proportional to a difference between the first andsecond encoded optical signals.

In some embodiments, the difference between the first and second encodedoutput signals is proportional to the second numeric value.

In some embodiments, the difference between the first and second encodedoptical signals is proportional to the first numeric value.

In some embodiments, the first and second encoded optical signals areorthogonal to each other.

In some embodiments, respective phases of the first and second encodedoptical signals are uncorrelated.

In some embodiments, the first and second encoded optical signals havedifferent carrier frequencies.

In some embodiments, the first and second encoded optical signals have aconstant quadrature phase difference.

In some embodiments, wherein receiving the input optical signalcomprises receiving the input optical signal from an incoherent lightsource.

In some embodiments, the first and second encoded optical signals haveorthogonal polarizations.

In some embodiments, the first and second encoded optical signals aretemporally non-overlapping.

In some embodiments, generating the first and second encoded opticalsignals comprises passing the input optical signal through an opticalmodulator.

In some embodiments, generating the first and second encoded opticalsignals comprises setting a characteristic of the optical modulatorbased on the first numeric value.

In some embodiments, obtaining the result comprises subtracting thefirst encoded output signal from the second encoded output signal orsubtracting the second encoded output signal from the first encodedoutput signal.

In some embodiments, generating the first and second encoded outputsignals comprises detecting the first and second encoded optical signalsusing one or more modulatable detectors.

In some embodiments, generating the first and second encoded outputsignals comprises setting a characteristic of the one or moremodulatable detectors based on the second numeric value.

In some embodiments, the first and second encoded optical signals areconfined within different optical waveguides.

In some embodiments, obtaining the result comprises obtaining a productof the first numeric value times the second numeric value.

Some embodiments relate to a photonic processor comprising: a pluralityof differential optical encoders including first and second differentialoptical encoders; a first set of differential multipliers coupled to thefirst differential optical encoder; a second set of differentialmultipliers coupled to the second differential optical encoder; a firstreceiver coupled to the first set of differential multipliers; and asecond receiver coupled to the second set of differential multipliers.

In some embodiments, at least one of the plurality of differentialencoders comprises an optical modulator having a pair of optical outputports.

In some embodiments, at least one differential multiplier of the firstand second sets of differential multipliers comprises an opticalmodulator having a pair of optical output ports.

In some embodiments, the first and second sets of differentialmultipliers comprise modulatable detectors.

In some embodiments, the photonic processor further comprises an opticalorthogonalization unit placed between the first differential opticalencoder and the first set of differential multipliers.

In some embodiments, the optical orthogonalization unit comprises aserpentine-shaped optical waveguide.

In some embodiments, the optical orthogonalization unit comprises anoptical polarization rotator.

In some embodiments, the photonic processor further comprises a lightsource and an optical splitter tree coupling the light source to thefirst set of differential multipliers.

In some embodiments, the optical splitter tree lacks waveguidecrossings.

In some embodiments, the photonic processor further comprises acontroller configured to control the plurality of differential opticalencoders, wherein the controller comprises a plurality of transistors,and wherein the plurality of transistors and the plurality ofdifferential optical encoders share at least one layer of asemiconductor substrate.

Some embodiments relate to a method for fabricating a photonic processorcomprising: obtaining a semiconductor substrate; forming, on thesemiconductor substrate: a plurality of differential optical encodersincluding first and second differential optical encoders; a first set ofdifferential multipliers coupled to the first differential opticalencoder; a second set of differential multipliers coupled to the seconddifferential optical encoder; a first receiver coupled to the first setof differential multipliers; and a second receiver coupled to the secondset of differential multipliers.

In some embodiments, forming the plurality of differential encoderscomprises forming a plurality of optical modulators each having a pairof optical output ports.

In some embodiments, the method further comprises forming a plurality oftransistors on the semiconductor substrate.

In some embodiments, the plurality of transistors and the plurality ofdifferential optical encoders share at least one layer of thesemiconductor substrate.

Some embodiments relate to a method for performing a mathematicaloperation comprising: receiving an input optical signal; obtaining afirst numeric value and a second numeric value; generating an encodedoptical signal by modifying the input optical signal using the firstnumeric value; generating a photocurrent at least in part by: detectingthe encoded optical signal using a modulatable detector, and setting acharacteristic of the modulatable detector based on the second value;and obtaining a result of the mathematical operation using thephotocurrent.

In some embodiments, the modulatable detector comprises a photodetector,and wherein setting the characteristic of the modulatable detector basedon the second value comprises setting a responsivity of thephotodetector based on the second value.

In some embodiments, obtaining the result comprises obtaining a productof the first numeric value times the second numeric value.

In some embodiments, the modulatable detector comprises a controlcapacitor, and wherein setting the characteristic of the modulatabledetector comprises setting a voltage applied to the control capacitor.

In some embodiments, the control capacitor comprises ametal-oxide-semiconductor capacitor (MOS cap), and wherein setting thevoltage applied to the control capacitor comprises setting the voltageapplied to the MOS cap.

In some embodiments, setting the characteristic of the modulatabledetector comprises producing carrier avalanche.

In some embodiments, generating the encoded optical signal comprisespassing the input optical signal through an optical modulator.

In some embodiments, the modulatable detector comprises a photodetectorand a transistor, and wherein setting the characteristic of themodulatable detector comprises setting a voltage applied to thetransistor.

In some embodiments, the modulatable detector comprises a photodetectorand a gain stage, and wherein setting the characteristic of themodulatable detector based on the second value comprises setting acurrent gain of the gain stage based on the second value.

Some embodiments relate to a photonic device configured to perform amathematical operation comprising: an optical encoder; a modulatabledetector coupled to an output of the optical encoder; and a controllercoupled to both the optical encoder and the modulatable detector, thecontroller being configured to: obtain a first numeric value and asecond numeric value, control the optical encoder to generate an encodedoptical signal by modifying an input optical signal using the firstnumeric value, control the modulatable detector to generate aphotocurrent in response to receiving the encoded optical signal,wherein controlling the modulatable detector comprises setting acharacteristic of the modulatable detector based on the second numericvalue, and obtain a result of the mathematical operation using thephotocurrent.

In some embodiments, the modulatable detector comprises a photodetector,and wherein setting the characteristic of the modulatable detector basedon the second value comprises setting a responsivity of thephotodetector based on the second value.

In some embodiments, the modulatable detector comprises aphoto-absorption region and a control capacitor positioned adjacent tothe photo-absorption region.

In some embodiments, the control capacitor comprises ametal-oxide-semiconductor capacitor (MOS cap).

In some embodiments, the modulatable detector further comprises anelectron avalanche region positioned adjacent to the MOS cap.

In some embodiments, the modulatable detector comprises: a firstphotodetector and a second photodetector; first and second transistorsboth coupled to the first photodetector; and third and fourthtransistors both coupled to the second photodetector.

In some embodiments, the first photodetector is coupled to respectivesources of the first and second transistors, and wherein the firsttransistor and the third transistor have drains that are coupled to eachother.

In some embodiments, the first and third transistors are arranged as aninverter, and wherein the first photodetector is coupled to respectivesources of the first and second transistors.

In some embodiments, the first photodetector is further coupled to thethird and fourth transistors and the second photodetector is furthercoupled to the first and second transistors, and wherein the firsttransistor and the second transistor have drains that are coupled toeach other and sources that are coupled to each other.

In some embodiments, the modulatable detector comprises: a firstphotodetector and a second photodetector; first and second transistorsboth coupled to the first photodetector; and a node coupled to the firstand second photodetectors and further coupled to the first and secondtransistors.

In some embodiments, the modulatable detector comprises a photodetectorand a plurality of transistors, and wherein the photodetector and theplurality of transistors are formed on a common semiconductor substrate.

In some embodiments, the modulatable detector comprises a plurality ofbalanced photodetectors and a plurality of transistors arrangeddifferentially.

Some embodiments relate to a photonic processor comprising: a pluralityof differential optical encoders including first and second differentialoptical encoders; a first pair of modulatable detectors coupled to thefirst differential optical encoder; a second pair of modulatabledetectors coupled to the second differential optical encoder; a firstdifferential receiver coupled to the first pair of modulatabledetectors; and a second differential receiver coupled to the second pairof modulatable detectors.

In some embodiments, at least one of the first pair of modulatabledetectors comprises a photo-absorption region and a control capacitorpositioned adjacent to the photo-absorption region.

In some embodiments, the control capacitor comprises ametal-oxide-semiconductor capacitor (MOS cap).

In some embodiments, at least one of the first pair of modulatabledetectors comprises: a first photodetector and a second photodetector;first and second transistors both coupled to the first photodetector;and third and fourth transistors both coupled to the secondphotodetector.

In some embodiments, the first photodetector is coupled to respectivesources of the first and second transistors, and wherein the firsttransistor and the third transistor have drains that are coupled to eachother.

In some embodiments, at least one of the first pair of modulatabledetectors comprises: a first photodetector and a second photodetector;first and second transistors both coupled to the first photodetector;and a node coupled to the first and second photodetectors and furthercoupled to the first and second transistors.

In some embodiments, at least one of the first pair of modulatabledetector comprises a photodetector and a plurality of transistors,wherein the photodetector and the plurality of transistors are formed ona common semiconductor substrate.

Some embodiments relate to a method for fabricating a photonic processorcomprising: obtaining a semiconductor substrate; forming, on thesemiconductor substrate: a plurality of differential optical encodersincluding first and second differential optical encoders; a first pairof modulatable detectors coupled to the first differential opticalencoder; a second pair of modulatable detectors coupled to the seconddifferential optical encoder; a first differential receiver coupled tothe first pair of modulatable detectors; and a second differentialreceiver coupled to the second pair of modulatable detectors.

In some embodiments, forming the plurality of differential encoderscomprises forming a plurality of optical modulators each having a pairof optical output ports.

In some embodiments, forming the first pair of modulatable detectorscomprising forming a plurality of transistors.

In some embodiments, the plurality of transistors and the plurality ofdifferential optical encoders share at least one layer of thesemiconductor substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the application will be describedwith reference to the following figures. It should be appreciated thatthe figures are not necessarily drawn to scale. Items appearing inmultiple figures are indicated by the same reference number in thefigures in which they appear.

FIG. 1A is a block diagram illustrating a dual-rail optical multiplier,in accordance with some embodiments.

FIG. 1B is a flow chart illustrating a method for performingmultiplications using a dual-rail optical multiplier, in accordance withsome embodiments.

FIG. 2A is a diagram illustrating a tunable directional coupler, inaccordance with some embodiments.

FIG. 2B is a diagram illustrating a portion of the tunable directionalcoupler of FIG. 2A in additional detail, in accordance with someembodiments.

FIG. 3 is a diagram illustrating a Mach-Zehnder interferometer, inaccordance with some embodiments.

FIG. 4A-4D are block diagrams illustrating additional dual-rail opticalmultiplier, in accordance with some embodiments.

FIG. 5 is a representation of a matrix-vector multiplication, inaccordance with some embodiments.

FIG. 6 is a block diagram of a photonic processor arranged according toa 2×2 configuration, in accordance with some embodiments.

FIG. 7A is a block diagram of a photonic processor arranged according toa 4×4 configuration, in accordance with some embodiments.

FIG. 7B is a diagram illustrating an optical splitter tree, inaccordance with some embodiments.

FIG. 8 is a diagram illustrating another optical splitter tree, inaccordance with some embodiments.

FIG. 9A is a block diagram illustrating a modulatable detector, inaccordance with some embodiments.

FIG. 9B is a block diagram illustrating a pair of modulatable detectorsarranged differentially, in accordance with some embodiments.

FIG. 9C-9D are block diagrams illustrating the interior of modulatabledetectors, in accordance with some embodiments.

FIG. 10A is a block diagram illustrating an optical multiplier includingthe modulatable detector of FIG. 9A, in accordance with someembodiments.

FIG. 10B is a flow chart illustrating a method for performingmultiplications, in accordance with some embodiments.

FIG. 11 is a block diagram illustrating a differential opticalmultiplier including the modulatable detectors of FIG. 9B, in accordancewith some embodiments.

FIG. 12A is a block diagram of another photonic processor arrangedaccording to a 2×2 configuration, in accordance with some embodiments.

FIG. 12B is a block diagram of another photonic processor arrangedaccording to a 4×4 configuration, in accordance with some embodiments.

FIG. 12C is a diagram illustrating an optical splitter tree, inaccordance with some embodiments.

FIG. 13 is a diagram illustrating a photoconductor, in accordance withsome embodiments.

FIG. 14A is a top view of a photodetector including ametal-oxide-semiconductor capacitor (MOS cap), in accordance with someembodiments.

FIG. 14B is a cross sectional view of the modulatable detector of FIG.14A taken along the BB line, in accordance with some embodiments.

FIG. 14C is an energy band diagram plotted along the CC line of FIG.14B, in accordance with some embodiments.

FIGS. 15A-15E are plots illustrating example responsivities for themodulatable detector of FIG. 14A, in accordance with some embodiments.

FIGS. 16A-16B are plots illustrating photocarrier concentration overtime, in accordance with some embodiments.

FIG. 17 is a plot illustrating example current/voltage characteristicsof a modulatable detector, in accordance with some embodiments.

FIGS. 18A-18H are circuit diagrams illustrating additional modulatabledetectors, in accordance with some embodiments.

FIGS. 19A-19B are plots illustrating example responsivities associatedwith the modulatable detector of FIG. 18E, in accordance with someembodiments.

FIGS. 20A-20B are cross sectional views illustrating substratesincluding modulatable detectors, in accordance with some embodiments.

DETAILED DESCRIPTION I. Overview

Conventional electronic processors face severe speed and efficiencylimitations primarily to the inherent presence of impedance inelectronic interconnects. Connecting multiple processor cores and/orconnecting a processor core to a memory involves use of conductivetraces. Large values of impedance limit the maximum rate at which datacan be transferred through the trace with a negligible bit error rate.For processing that requires billions of operations, these delays canresult in a significant loss of performance. In addition to electricalcircuits' inefficiencies in speed, the heat generated by the dissipationof energy caused by the impedance of the circuits is also a barrier indeveloping electronic processors.

The inventors have recognized and appreciated that using optical signals(instead of, or in combination with, electrical signals) overcomes theaforementioned problems with electronic computing. Optical signalstravel at the speed of light in the medium in which the light istraveling. Thus, the latency of optical signals is far less of alimitation than electrical propagation delay. Additionally, no power isdissipated by increasing the distance traveled by the light signals,opening up new topologies and processor layouts that would not befeasible using electrical signals. Thus, photonic processors offer farbetter speed and efficiency performance than conventional electronicprocessors.

The inventors have recognized and appreciated that photonic processorsare well-suited for particular types of algorithms. For example, manymachine learning algorithms (e.g. support vector machines, artificialneural networks and probabilistic graphical model learning) rely heavilyon linear transformations on multi-dimensional arrays/tensors. Thesimplest linear transformation is a matrix-vector multiplication, whichusing conventional algorithms has a complexity on the order of O(N²),where N is the dimensionality of a square matrix being multiplied by avector of the same dimension. The inventors have recognized andappreciated that a photonic processor can perform lineartransformations, such as matrix multiplication, in a highly parallelmanner by propagating a particular set of input optical signals througha configurable array of active optical components. Using suchimplementations, matrix-vector multiplication of dimension N=512 can becompleted in hundreds of picoseconds, as opposed to the tens to hundredsof nanoseconds using conventional electronic circuit-based processing.

General matrix-matrix (GEMM) operations are ubiquitous in softwarealgorithms, including those for graphics processing, artificialintelligence, neural networks and deep learning. GEMM calculations intoday's computers are typically performed using transistor-based systemssuch as GPU systems or systolic array systems. Matrix-vectormultiplication using photonics arrays can be highly power efficient whencompared to their electronic counterparts as optical signals canpropagate within a semiconductor substrate with a minimal amount ofloss.

However, the inventors have recognized and appreciated a number ofchallenges associated with the use of such photonic arrays. First, justlike electronic circuits, photonic arrays are susceptible to noise.Noise arises in photonic arrays due to a variety of mechanisms,including thermal noise and shot noise. The presence of noise reducesthe ability of photonic arrays to accurately reproduce and processnumeric values, thereby reducing their overall performance.

Second, photonic arrays are susceptible to optical loss. On the onehand, optical sources can produce only limited amounts of optical power.On the other hand, photodetectors are limited by shot noise, meaningthat the minimum optical power that a photodetector can detect islimited to a floor level. The result is that the optical power budget islimited, and therefore, every decibel of optical power counts. Opticalloss negatively affects the power budgets, and can arise due to avariety of reasons. For example, optical loss arises as a result ofoptical modulation. In conventional optical systems, optical power isintentionally attenuated—thereby increasing optical loss—to producemodulation. For example, in amplitude-based modulation schemes, alogical 0 is reproduced by suppressing the power of an optical signal.

Third, conventional photonic arrays occupy substantially more chip realestate than electronic components such as transistors, thereby limitingthe amount of processing capabilities that may be integrated on a singlechip. Consider for example Mach-Zehnder interferometers, which areconventionally used to perform optical modulation. To provide sufficientoptical modulation, Mach-Zehnder interferometers are generally designedwith large lengths, often in the order of several millimeters. One theother hand, a transistor, the core component of an electronic circuit,is several orders of magnitude smaller.

The inventors have developed a novel photonic processing architecturefor performing matrix-matrix multiplication (including matrix-vectormultiplication, a core component of GEMM operations), that avoids ormitigates the above-described challenges. According to an aspect of thepresent disclosure, the architecture described herein involvesprocessing optical signals in a differential fashion. Instead ofencoding data into a single-ended optical signal as is done for examplein digital optical communication systems, data is encoded in thedifference between a pair of optical signals (e.g., in the differencebetween the amplitudes of the optical signals or in the differencebetween the powers of the optical signals). This architecture isreferred to herein as “dual-rail.” One rail carries an optical signal,another rail carries another optical signal. Rails can be implemented inany of numerous ways, including for example using a pair of distinctoptical waveguides, where each waveguide carries one optical signal. Itshould be appreciated, however, that the rails need not be physicallyseparate channels. In some embodiments, for example, both rails areimplemented on the same physical waveguide, and the optical signals aredistinguishable from one another by virtue of their polarization,wavelength, or other optical characteristics.

The dual-rail architectures described herein reduce photonicprocessors'susceptibility to noise. Statistically, when noise is presenton the first rail, there is a high likelihood that noise havingsubstantially the same characteristics is also present on the secondrail. This is especially true if the rails are defined on opticalwaveguides positioned in close proximity to one another. Decoding dataencoded on the difference between the optical signals of the railsinvolves performing a subtraction, meaning that the signal (includingnoise) present at the first rail is subtracted from the signal(including noise) present at the second rail. If the noise present atthe first rail has characteristics substantially similar to the noisepresent at the second rail (e.g., there is a relatively highcorrelation), the overall noise is reduced when the subtraction isperformed.

In addition to improving the susceptibility to noise, the dual-railarchitectures described herein reduce modulation-induced optical loss.Unlike in conventional optical digital communication systems, in whichoptical modulation is achieved by introducing optical attenuation,optical modulation according to the present architectures involves arotation of the optical vector (phase and/or polarization). In otherwords, modulation involves manipulating the relative phase of theoptical signals present at the two rails. This results in a substantialreduction of the optical loss.

According to another aspect of the present disclosure, the photonicarchitectures described herein involve multipliers implemented based on“modulatable detectors.” Modulatable detectors are optical detectorshaving at least one characteristic that can be controlled by a userusing one or more electric control signals. These detectors are designedso that application of a control signal (e.g., a voltage or a current)alters a characteristic of the detector, such as the detector'sresponsivity, gain, impedance, etc. The result is that the detector'sphotocurrent (the current that the modulatable detector produces inresponse to light) depends not only on the optical power incident on thedetector, but also on the control signal applied to the detector. Thismay be achieved in any of numerous ways, as described in detail furtherbelow. In one example, a modulatable detector is designed to include acontrol capacitor. The control capacitor is designed so that a change inthe voltage applied to it results in a change in the responsivity of themodulatable detector. The control capacitor may be implemented, amongother possible configurations, using a pair of electrodes separated by adielectric material or using a metal-oxide-semiconductor capacitor (MOScap). In another example, a modulatable detector includes aphotodetector and a gain stage coupled to the photodetector. The gainstage may be connected to the photodetector so that a change in thevoltage applied to the gain stage produces a change in the photocurrentgenerated by the modulatable detector. Several examples of controllablegain stages are described in detail further below.

Photonic arrays that use modulatable detector-based multipliers aresubstantially more compact than other types of photonic arrays. This isbecause modulatable detectors are far more compact than optical devicestraditionally used to perform multiplication in the optical domain, suchas phase shifters (e.g., Mach-Zehnder interferometers), attenuators andamplifiers.

II. Dual-Rail Optical Multipliers

FIG. 1A is a block diagram illustrating an optical multiplierimplemented based on a dual-rail architecture, in accordance with someembodiments. This optical multiplier includes a light source 10, adifferential optical encoder 12, a differential optical multiplier 14, adifferential receiver 16 and a controller 17. Controller 17 includes apair of digital-to-analog converters (D/A) 19 and a numeric value unit18.

Numeric value unit 18 produces a pair of scalar numeric values: x and m.Numeric value m is also referred to as “weight” or “weight parameter”and numeric value x is also referred to herein as “input data,” “inputvalue” or “input parameter”. These numeric values may be produced basedon data received by the controller, including data obtained from amemory internal to controller 17 and/or data provided to controller 17from another computing system. These numeric values may be representedusing any digital representation, including fixed-point orfloating-point representations. The first D/A 19 converts numeric valuex to an electric signal representative of x. In this example, the D/Aproduces a voltage V_(x). The second D/A 19 converts numeric value m toan electric signal representative of m. In this example, the D/Aproduces a voltage V_(m). In some embodiments, V_(x) is proportional tox. In some embodiments, V_(m) is proportional to m. The dual-railoptical multiplier of FIG. 1A is configured to multiply these numericvalues to one another, thereby producing the result x×m.

Light source 10 may be implemented using a coherent source, e.g., alaser. Alternatively, light source 10 may be implemented using anincoherent source, e.g., a light-emitting diode, a source of amplifiedspontaneous emission, or a source of stimulated emission having arelatively large linewidth. As used herein, the terms “coherence” and“coherent” refers to temporal coherence. The optical power produced bylight source 10 is identified as “P_(in).”

Differential optical encoder 12 receives a voltage V_(x), and inresponse, produces a pair of optical signals. The labels “P_(t)” and“P_(b)” identify the optical powers of these optical signals,respectively. Differential optical encoder 12 receives voltage V_(x),and encodes the optical signal received from light source 10 based on V.More specifically, differential optical encoder 12 produces a pair ofoptical signals in such a way that the difference between the powers ofthese optical signals (P_(t)−P_(b)) is proportional to both x and Pin(in FIG. 1A, the symbol “∝” means “is proportional to”). It should beappreciated that this architecture is referred to as “dual-rail” in thatx is encoded in the difference between two optical signals (thedifference in the signal powers as in this example, or in otherexamples, the difference between the signal amplitudes). Differentialoptical encoder 12 may be implemented using any suitable opticalmodulator, including an optical interferometer (such as a tunabledirectional coupler or a Mach-Zehnder interferometer), a resonantmodulator, a Franz-Keldysh modulator, etc. Examples of differentialoptical encoder 12 are described in detail further below.

As discussed above, P_(t) identifies the power of the optical signal atthe top rail and P_(b) identifies the power of the optical signal at thebottom rail. In some embodiments, the rails are defined in terms ofphysical channels. In one example, the top rail is defined in a firstoptical waveguide and the bottom rail is defined in a second opticalwaveguide that is physical distinct from the first optical waveguide. Inanother example, the top rail is defined in a first free-space opticalchannel and the bottom rail is defined in a second free-space opticalchannel that is spatially separated from the first free-space opticalchannel. In other embodiments, however, the top and bottom rails may bedefined by a common physical channel. That is, the optical signalsgenerated by differential optical encoder 12 share the same opticalwaveguide or free-space channel. In these embodiments, the opticalsignal of each rail is distinguishable from the optical signal of theother rail by a certain optical characteristic, such as by the time bin,polarization or wavelength. In one example, the optical signal at thefirst rail is defined by a first polarization mode of an opticalwaveguide (e.g., the optical waveguide's TE₀₀-mode) and the opticalsignal at the second rail is defined by a second polarization mode ofthe same optical waveguide (e.g., the optical waveguide's TE₀₁-mode orTM₀₀-mode). In another example, the optical signal at the first rail isdefined by a first wavelength and the optical signal at the second railis defined by a second wavelength.

It should be appreciated that, while FIG. 1A depicts an architecture inwhich the signals representing the numeric values to be multiplied arevoltages (V_(x) and V_(m)), in other embodiments, the numeric values maybe represented using other types of electrical signals, such as electriccurrents or electric charges.

Differential optical multiplier 14 receives the optical signals producedby differential optical encoder 12 and produces a pair of output opticalsignals based on the voltage V_(m). The powers of the output opticalsignals are labeled “P_(t)′” and “P_(b)′,” respectively. The opticalsignals produced by differential optical multiplier 14 are such that thedifference between their powers (P_(t)′−P_(b)′) is proportional to bothm and the difference P_(t)−P_(b). The result is that the quantityP_(t)′-P_(b)′ is proportional to each of m, x and P_(in). Beingproportional to both x and m, P_(t)′−P_(b)′, in essence, is encoded withthe product of numeric value x times numeric value m.

Differential optical multiplier 14 may be implemented using any suitablephotonic device, including any suitable optical interferometer such asan adjustable directional coupler or a Mach-Zehnder interferometer, asdescribed in detail further below.

Differential receiver 16 detects optical signals P_(t)′ and P_(b)′ and,in response, produces a numeric value y that is equal to the productx×m. To perform this operation, receiver 16 may include for example apair of balanced photodetectors, a differential trans-impedanceamplifier configured to generate an output voltage proportional toP_(t)′−P_(b)′, and an analog-to-digital converter configured to convertthe output voltage to a numeric value y.

FIG. 1B is a flow chart illustrating a method for performingmathematical operations (e.g., multiplications), in accordance with someembodiments. Method 20 can be performed using any suitable opticaldevice, including the dual-rail architecture depicted in FIG. 1A. Method20 begins at step 22, in which an optical device receives an inputoptical signal. Referring for example to the architecture of FIG. 1A, atstep 22, differential optical encoder 12 receives the optical signalP_(in).

At step 24, the photonic device obtains a first numeric value and asecond numeric value. These are the numeric values to be multiplied. Thenumeric values need not be obtained at the same time. Referring forexample to the architecture of FIG. 1A, at step 24, numeric value unit18 generates numeric values x and m based on data stored in a memory ofcontroller 17 and/or on data obtained from another computing system.These numeric values may represent any type of information, such astext, audio, video, etc. The numeric values may be real or complex,positive or negative.

At step 26, the photonic device generates a pair of encoded opticalsignals by modifying the input optical signal using the first numericvalue. In some embodiments, the pair of encoded optical signals areencoded so that the difference between the optical signals (e.g., thedifference between the powers of the optical signals or the differencebetween the amplitudes of the optical signals) is proportional to thefirst numeric value. Referring for example to the architecture of FIG.1A, at step 26, differential optical encoder 12 generates opticalsignals with powers P_(t) and P_(b), respectively, based on numericvalue x.

At step 28, the photonic device generates a pair of encoded outputsignals using the second numeric value and the pair of encoded opticalsignals generated at step 26. In some embodiments, the difference (interms of power or amplitude) between the first and second encoded outputsignals is proportional to the difference (again, in terms of power oramplitude) between the first and second encoded input signals. In somesuch embodiments, the difference between the first and second encodedoutput signals is proportional to both the second numeric value and thefirst numeric value. Referring for example to the architecture of FIG.1A, at step 28, differential optical multiplier 14 generates opticalsignals with powers P_(t)′ and P_(b)′, respectively, based on numericvalue m and P_(t)−P_(b).

At step 30, the photonic device obtains a result of a mathematicaloperation (e.g., the product of the first numeric value times the secondnumeric value) using the pair of encoded output signals. In someembodiments, step 30 involves i) detecting the pair of encoded outputsignals with a pair of balanced photodetectors to obtain a pair ofphotocurrents, ii) receiving the photocurrents with a differentialtrans-impedance amplifier to obtain an output voltage, and iii)converting the output voltage with an analog-to-digital converter toobtain a numeric value representing the result (e.g., the product).Referring for example to the architecture of FIG. 1A, at step 30,differential receiver 16 generates numeric value y, which equals theproduct of x times m.

As discussed above, differential optical multiplier 14 may beimplemented using any suitable optical device. One such device is thetunable directional coupler depicted in FIG. 2A, in accordance with someembodiments. The directional coupler includes a pair of input opticalwaveguides, where one input optical waveguide receives optical signalP_(t) and the other input optical waveguide receives optical signalP_(b). The directional coupler further includes a pair of output opticalwaveguides, where one output optical waveguide outputs optical signalP_(t)′ and the other output optical waveguide outputs optical signal K.The region between the pair of input of optical waveguides and the pairof output optical waveguides is labeled “A.” This is the region in whichthe input optical signals are combined to produce the output opticalsignals.

Region A is depicted in additional detail in FIG. 2B. In this region,the waveguides are sufficiently close to one another to produceevanescent coupling. The coupling coefficient with which the waveguidescouple to one another depends, among other parameters, on the spatialdistance d between the waveguides. The closer the waveguides, the largerthe coupling coefficient. In some embodiments, the directional couplermay be designed so that d is adjustable based on an input signal. Thismay be achieved using nano-opto-electro-mechanical system (NOEMS)techniques. For example, the waveguides may be suspended in air in theregion A, and the position of the suspended waveguides in the lateraldirection (the direction in the plane of the waveguides perpendicular tothe propagation axis) can be controlled with an external voltage.Referring again to FIG. 1A, voltage V_(m) may control the distancebetween the waveguides in region A.

Referring back to FIG. 2A, the letter “t” identifies the transmissioncoefficient and the letter “k” identifies the cross-coupling coefficient(from one waveguide to the other). The coefficients t and k areexpressed in terms of amplitude transmission, and must obey therelationship |t|²+|k|²≤1 in order to provide for energy conservation.The equality is achieved when the multiplication device is lossless.Coefficients t and k depend on the distance between the waveguides d.Accordingly, voltage V_(m) controls the coefficients t and k.

The power P_(t)′ is equal to the fraction of P_(t) that travels on thetop waveguide (equal to |t|² P_(t)), plus the fraction of P_(b) thatcouples to the top waveguide (equal to |k|² P_(b)), plus a cross termresulting from the interference of the signal at the top waveguide withthe signal at the bottom waveguide. It should be appreciated that theinterference term is non-zero if the input optical fields are coherentto one another (in other words, their phases are correlated). However,if the input optical signals are not mutually coherent, the interferenceterm goes to zero. This is because mutually incoherent optical signals,having uncorrelated phases, do not interfere with each other. Therefore,assuming that the signals are not mutually coherent, the output power atthe top waveguide is simply given by |t|²P_(t) +|k|²P_(b). Similarly,the power P_(b)′ is equal to the fraction of P_(b) that travels on thebottom waveguide (equal to |t|²P_(b)), plus the fraction of P_(t) thatcouples to the bottom waveguide (equal to |k|²P_(t)), plus a cross termresulting from the interference of the signal at the bottom waveguidewith the signal at the top waveguide. Again, the interference term isnon-zero if the input optical fields are coherent to one another.However, if the input optical signals are not mutually coherent, theinterference term goes to zero. Therefore, assuming that the signals arenot mutually coherent, the output power at the bottom waveguide issimply given by |t|²P_(b)+|k|²P_(t).

As discussed above, in dual-rail architectures of the types describedherein, numeric values are encoded in the difference (power differenceor amplitude difference) between optical signals. When the input signalsare mutually incoherent, the difference P_(t)′−P_(b)′ is equal to(|t|²−|k|²)(P_(t)−P_(b)). It should be noted that, when the inputsignals are mutually incoherent, the directional coupler of FIG. 2Aoperates as an optical multiplier in that it outputs the product of thequantity |t|²−|k|²times the quantity P_(t)−P_(b). However, thedirectional coupler does not output the product if the input signals aremutually coherent. Therefore, it is critical that the input signals bemutually incoherent.

Mutual incoherence may be achieved in a variety of ways. First, mutualincoherence may be achieved by using an incoherent light source, such asan LED, a source of amplified spontaneous emission or a source ofstimulated emission with a relatively large linewidth. Second, mutualincoherence may be achieved by allowing one waveguide (e.g., the topwaveguide) to travel a distance greater that the distance traveled bythe other waveguide (e.g., the bottom waveguide), where the differencebetween the distances is greater that the coherence length of the lightsource (as discussed in detail below in connection with FIG. 4C).

Additionally, or alternatively, differential optical encoder 12 mayimplemented in some embodiments using the directional coupler of FIG.2A. In such embodiments, the top input waveguide receives P_(in), andthe bottom input waveguides receives no optical signal (though theopposite is also possible). The output waveguides output, respectively,P_(t)=|t|²P_(in) and P=|k|² P_(in), where t and k are controlled usingvoltage V_(x) (that is, by controlling distance d).

Another implementation of differential optical multiplier 14 is depictedin FIG. 3 , in accordance with some embodiments. This embodimentsincludes a Mach-Zehnder interferometer. In this example, thecoefficients t and k are controlled based on the phases (pi andintroduced by the phase shifters (which in turn are controlled based onvoltage V_(m)). The differential output optical power is in generalgiven by: ΔP ∝sin (θ_(v)) cos (θ_(w))+2 cos φ[cos (θ_(w)/2) sin(θ_(w)/2) (cos²(θ_(v)/2)−sin² (θ_(v)/2))], where φ is the differencebetween φ₁ and φ₂. However, when an incoherent light source is used orwhen the light source has a coherence length shorter than the opticaldelay line, the phase term cos (φ) time-averages to zero. This leaves ΔP∝sin (θ_(v)) cos (θ_(w))Therefore, the difference between the powers ofthe output optical signals is proportional to a product.

Both the implementations of FIG. 2A and FIG. 3 produce differentialoptical multiplication assuming that the input optical signals aremutually incoherent. This is because, when the signals are mutuallyincoherent, the interference term is zero. It should be noted that thereare other ways to cause the interference term to be zero. For example,the interference term can be set to zero by defining the input opticalsignals on mutually orthogonal polarizations. Additionally, oralternatively, the interference term can be set to zero by defining theinput optical signals on non-overlapping time bins. Additionally, oralternatively, the interference term can be set to zero by defining theinput optical signals on different carrier frequencies.

The architecture of FIG. 4A is designed to cause the signals P_(t) andP_(b) to be combined to one another so that the interference term iszero. In addition to the architecture of FIG. 1A, this architecturefurther includes optical orthogonalization unit 13. Opticalorthogonalization unit 13 is configured to render signals P_(t) andP_(b) orthogonal to one another. Here, two signals are orthogonal if,when the signals are combined, the resulting interference term issubstantially zero. In the example of FIG. 4B, optical orthogonalizationunit 13 includes optical polarization rotator 43. In this example,optical signals P_(t) and P_(b) are orthogonal in that they are definedon orthogonal polarizations.

In the example of FIG. 4C, optical orthogonalization unit 13 includes anoptical delay line 45 (e.g., a serpentine-shaped waveguide). Here, theoptical delay line is introduced to delay signal P_(t) relative tosignal P_(b) by a sufficient amount to render the phases of the signalsmutually uncorrelated. To achieve this result, the additional pathintroduced by optical delay line 45 must be greater than the coherencelength of the light source. In some embodiments, the optical delay linemay be sized to provide a constant quadrature phase difference.

Alternatively, or additionally, the optical delay line is introduced todelay signal P_(t) relative to signal P_(b) by a sufficient amount sothat the signals do not overlap in time (are defined in different timebins). To achieve this result, the additional delay introduced byoptical delay line 45 must be greater than the duration of the signalpulses.

In another example, optical orthogonalization unit 13 includes a devicefor defining the first rail on one carrier frequency and the second railon another carrier frequency. This may be achieved, in some embodiments,using an optical non-linear medium. Alternatively, distinct carrierfrequencies may be obtained by using two distinct lasers that emit atdifferent wavelengths. The first laser emits at a first wavelength andsupports the first rail, the second laser emits at a second wavelengthand supports the second rail.

FIG. 4D depicts an implementation of the architecture of FIG. 4C, inaccordance with some embodiments. Here, both differential opticalencoder 12 and differential optical multiplier 14 are implemented usingMach-Zehnder interferometers 70. Each Mach-Zehnder interferometerincludes a phase shifter 72. The phase shifter of differential opticalencoder 12 is controlled using voltage V_(x) and the phase shifter ofdifferential optical multiplier 14 is controlled using voltage V_(m).

III. Photonic Processors Using Dual-Rail Multipliers

The dual-rail multiplier of FIG. 1A performs scalar multiplications (xtimes m). However, many machine learning algorithms rely onmatrix-matrix (e.g., matrix-vector) multiplication. Some embodimentsrelate to photonic processors configured to perform matrix-matrix (e.g.,matrix-vector) multiplications using the dual-rail optical multipliersdescribed above. These photonic processors are configured to multiply amatrix M by a vector X to produce a vector Y. Matrix M is also referredto herein as “weight matrix,” vector X is also referred to herein as“input vector” and vector Y is also referred to herein as “outputvector.” FIG. 5 illustrates an example of such a multiplication. In thisexample, M is an N×N matrix, though embodiments of the presentapplication are not limited to square matrices or to any specificdimension.

An example of a dual-rail photonic processor is depicted in FIG. 6 , inaccordance with some embodiments. In this implementation, the photonicprocessor is configured to multiply a 2×2 matrix (M) by a 2×1 inputvector (X) to obtain a 2×1 output vector (Y). A first light source 10provides an input optical signal having power P_(in1) and a second lightsource 10 provides an input optical signal having power P_(in2)(although the same light source may be used in some embodiments).P_(in2) may be equal to or different from P_(in1). Each light source isfollowed by a differential optical encoder 12, which operates in themanner described in connection with the differential optical encoder ofFIG. 1A. The first differential optical encoder receives voltage V_(x1),which is representative of numeric value x₁. This differential opticalencoder encodes the received input optical signal using voltage V_(x1)to generate a pair of encoded optical signals having powers P_(t1) andP_(b1). These optical signals are provided as inputs to two differentialoptical multipliers 14. The top differential optical multiplier receivesvoltage V_(M11), which represents numeric value M₁₁. The bottomdifferential optical multiplier receives voltage V_(M21), whichrepresents numeric value M₂₁. Both differential optical multipliersoperate in the manner described in connection with the differentialoptical multiplier of FIG. 1A. The top differential optical multiplieroutputs optical signals Pb₁₁′ and Pt_(11,′) and the bottom differentialoptical multiplier outputs optical signals Pb₂₁′ and Pt₂₁′. Thedifference between Pb₁₁′ and Pt₁₁′ is proportional to both M₁₁ and thedifference between Pb₁ and Pt₁, and accordingly, is proportional to theproduct M₁₁x₁. Similarly, the difference between Pb_(21′) and Pt₂₁ isproportional to both M₂₁ and the difference between Pb₁ and Pt₁, andaccordingly, is proportional to the product M₂₁x₁. The four outputoptical signals are detected using respective photodetectors 60.

The second differential optical encoder receives voltage V_(x2), whichis representative of numeric value x₂. This differential optical encoderencodes the received input optical signal using voltage V_(x2) togenerate a pair of encoded optical signals having powers P_(t2) andP_(b2). These optical signals are provided as inputs to two differentialoptical multipliers 14. The top differential optical multiplier receivesvoltage V_(M12), which represents numeric value M₁₂. The bottomdifferential optical multiplier receives voltage V_(M22), whichrepresents numeric value M₂₂. Both differential optical multipliersoperate in the manner described in connection with the differentialoptical multiplier of FIG. 1A. The top differential optical multiplieroutputs optical signals Pb₁₂′ and Pt₁₂′, and the bottom differentialoptical multiplier outputs optical signals Pb_(22′) and Pt_(22′). Thedifference between Pb₁₂′ and Pt₁₂′ is proportional to both Mu and thedifference between Pb₂ and Pt₂, and accordingly, is proportional to theproduct M₁₂x₂. Similarly, the difference between Pb₂₂′ and Pt₂₂′ isproportional to both M₂₂ and the difference between Pb₂ and Pt₂, andaccordingly, is proportional to the product M₂₂x₂. The four outputoptical signals are detected using respective photodetectors 60.

As shown in FIG. 6 , the outputs of the photodetectors are combined(see, e.g., node 62), thereby allowing the photocurrents to be added toone another. Receivers 64 receive the photocurrents produced bydetectors 60. Receivers 64 include a differential trans-impedanceamplifier (or other circuits for subtracting the first input currentfrom the second input current) and an analog-to-digital converter. Thetop receiver 64 outputs numeric value y₁₌M₁₁x₁+M₁₂x₂. The bottomreceiver 64 outputs numeric value y₂₌M₂₁x₁+M₂₂x₂.

An example of a 4×4 dual-rail photonic processor is illustrated in FIG.7A. This processor includes four light sources 10 (not shown), fourdifferential encoders 12 (which encode numeric values x₁, x₂, x₃ and x₄into respective pairs of dual-rail optical signals), four opticalsplitter trees 75 (shown in additional detail in FIG. 7B), sixteendifferential optical multipliers 14 (which multiply the respectiveinputs by M₁₁, M₂₁, M₃₁, M₄₁, M₁₂, M₂₂, M₃₂, M₄₂, M₁₃, M₂₃, M₃₃, M₄₃,M₁₄, M₂₄, M₃₄ and M₄₄), thirty-two detectors 60 and four receivers 64.

FIG. 7B illustrates a portion of the photonic processor of FIG. 7A inadditional detail. More specifically, FIG. 7B illustrates an opticalsplitter tree 75. Optical splitter tree 75 delivers the optical signalsproduced by a differential optical encoder 12 to multiple differentialoptical multipliers 14. In this implementation, the optical splittertree includes multiple 3db optical splitters 76 and multiple opticalwaveguide crossings 77. Each crossing may be implemented using twolevels of waveguides. For example, one waveguide level (e.g., the bottomlevel) may be made of silicon and another waveguide level (e.g., the toplevel) may be made of silicon nitride.

FIG. 8 illustrates an alternative optical splitter tree that does notinclude optical waveguide crossings. The inventors have recognized thatpassing light through a waveguide crossing leads to optical loss,thereby negatively affecting the overall performance of the photonicprocessor. The tree of FIG. 8 improves the performance of the photonicprocessor because waveguide crossings are omitted (another example ofsuch an optical splitter tree is described below in connection with FIG.12C).

IV. Optical Multipliers and Processors Based on Modulatable Detectors

The inventors have appreciated that some optical multipliers occupysubstantial chip real estate due to the presence of lengthy opticalinterferometers. This limits the number of multipliers that can beintegrated on a single chip, thus limiting the computationalcapabilities of photonic processors that employ these multipliers. Someembodiments relate to compact optical multipliers that are based onmodulatable detectors. Modulatable detectors are optical detectorshaving at least one characteristic that can be controlled by a userusing an electric control signal. These detectors are designed so thatvarying the magnitude of a control signal (e.g., a voltage or a current)alters a characteristic of the detector, such as the detector'sresponsivity, gain, impedance, conductance, etc. The result is that thedetector's photocurrent depends not only on the optical power that thedetector receives, but also on the control signal applied to thedetector. Optical multipliers based on modulatable detectors aredesigned so that one of the factors to be multiplied modulates themodulatable characteristic. For example, in some of the embodiments inwhich the modulatable characteristic is the detector's responsivity, theresponsivity may be controlled based on a weight parameter m.

FIG. 9A is a block diagram illustrating a modulatable detector, inaccordance with some embodiments. Modulatable detector 90 receives asinput an optical signal having power P, and in response, produces aphotocurrent i (the dark current of the modulatable detector will beneglected from this discussion). The photocurrent i is related to theinput optical power by the following expression: i=P/R, where R is theresponsivity of the modulatable detector. In addition to being dependentupon power P, the photocurrent is also dependent upon control voltage V(or, in other embodiments, another type of electric signal such acontrol current). This detector is preceded by the term “modulatable” toindicate that the photocurrent can be modulated through the applicationof a control electric signal. Example implementations of modulatabledetector 90 are described in detail further below.

FIG. 9B is a block diagram illustrating a pair of modulatable detectorsarranged according to a dual-rail architecture, in accordance with someembodiments. The top modulatable detector receives optical power P₊ andcontrol voltage V₁. Photocurrent ii depends upon optical power P₊ andcontrol voltage V₁. Similarly, the bottom modulatable detector receivesoptical power P⁻ and control voltage V₂. Photocurrent i₂ depends uponoptical power P⁻ and control voltage V₂.

FIG. 9C is a block diagram illustrating the interior of a modulatabledetector, in accordance with some embodiments. Modulatable detector 90includes a photodetector 91 and a gain stage 92. Photodetector 91 may beimplemented using a photoconductor, a photodiode, an avalanchephotodiode, a phototransistor, a photomultiplier (e.g., a tube), asuperconducting detector, a graphene-based detector, or any othersuitable type of photo-sensitive device. Gain stage 92 can include, forexample, a current amplifier for amplifying the current generated byphotodetector 91. In some embodiments, modulating a characteristic ofmodulatable detector 90 may involve modulating, using voltage V (orusing a control current), the responsivity of photodetector 91 and/orthe gain (e.g., current gain) or impedance of gain stage 92. FIG. 9D issimilar to the diagram of FIG. 9C, but illustrates a pair of modulatabledetectors arranged in a dual-rail configuration. As shown, eachphotodetector 91 is coupled to both gain stages 92.

FIG. 10A is a block diagram illustrating an optical multiplier based ona modulatable detector, in accordance with some embodiments. Just likethe multiplier of FIG. 1A, this multiplier includes a light source 10and a controller 17, which includes a pair of D/As 19 and a numericvalue unit 18.

Optical encoder 82 generates an encoded optical signal having power P,that is proportional to both numeric value x and input power P_(in).Optical encoder 82 may be implemented using any optical modulator,including an optical interferometer (e.g., a tunable directional coupleror a Mach-Zehnder interferometer), a resonant modulator, a Franz-Keldyshmodulator, etc.

Modulatable detector 90 multiplies numeric value x by numeric value m.This is achieved by producing a photocurrent i that is proportional toboth P_(x) and m (by way of voltage V_(m)), and accordingly, isproportional to P_(in, x) and m. Receiver 96 includes a trans-impedanceamplifier and an analog-to-digital converter. Receiver 96 produces anoutput numeric value y that is equal to the product of x times m.

FIG. 10B is a flow chart illustrating a method for performingmathematical operations (e.g., multiplications), in accordance with someembodiments. Method 200 can be performed using any suitable opticaldevice, including the modulatable detector-based optical multiplierdepicted in FIG. 10A.

Method 200 begins at step 202, in which an optical device receives aninput optical signal. Referring for example to the architecture of FIG.10A, at step 202, optical encoder 82 receives optical signal P_(in).

At step 204, the photonic device obtains a first numeric value and asecond numeric value. These are the numeric values to be multiplied. Thenumeric values need not be obtained at the same time. Referring forexample to the multiplier of FIG. 10A, at step 204, numeric value unit18 generates numeric values x and m based on data stored in a memory ofcontroller 17 and/or on data obtained from another computing system.These numeric values may represent any type of information, such astext, audio, video, etc. The numeric value may be real or complex,positive or negative.

At step 206, the photonic device generates an encoded optical signal bymodifying the input optical signal using the first numeric value.Referring for example to the multiplier of FIG. 10A, at step 206,optical encoder 82 produces an encoded optical signal having a powerproportional to both P_(in) and x.

At step 208, the photonic device generates a photocurrent. Thegeneration involves detecting the encoded signal using a modulatabledetector and setting a characteristic of the modulatable detector basedon the second numeric value. Referring for example to the multiplier ofFIG. 10A, at step 208, modulatable detector 90 produces photocurrent i,which involves detecting optical signal P_(x) and setting acharacteristic of the modulatable detector based on voltage V_(m).

At step 210, the photonic device obtains a result of the mathematicaloperation using the photocurrent. In some embodiments, the resultrepresents the product of the first numeric value times the secondnumeric value. In some embodiments, this step involves generating avoltage based on the photocurrent generated at step 208, and convertingthe voltage to the digital domain. Referring for example to themultiplier of FIG. 10A, step 210 may be performed using receiver 96.

The optical multiplier of FIG. 10A is based on a single-railarchitecture. In some embodiments, however, modulatable detector-basedoptical multipliers are arranged in accordance with a dual-railarchitecture. In this way, the multiplier further leverages the benefitsdescribed above in connection with FIG. 1A, including increased immunityto noise and reduced optical loss.

FIG. 11 is a block diagram of a dual-rail modulatable detector-basedoptical multiplier, in accordance with some embodiments. This opticalmultiplier combines the architecture of FIG. 1A with the architecture ofFIG. 10A. Differential optical encoder 12 produces a pair of encodedoptical signals having powers P_(t) and P_(b), respectively. Thedifference between the optical signals (e.g., the difference in signalpower or signal amplitude) is proportional to both numeric value x andinput power P_(in). This optical multiplier includes a pair ofmodulatable detectors 90. The top modulatable detector produces aphotocurrent i_(t), the bottom modulatable detector produces aphotocurrent i_(b). Photocurrent it depends on both optical power P_(t)and voltage V_(m). Similarly, photocurrent i_(b) depends on both opticalpower P_(b) and voltage −V_(m). The difference between it and i_(b) isproportional to both m and V_(t)−V_(b), and accordingly, is proportionalto P_(in), x and m. In some embodiments, the two modulatable detectorscan be coupled together as described in FIG. 9D such that bothphotocurrents it and ib depend on both optical powers Pt and Pb and Vm.In this configuration, the modulatable detectors steer the photocurrentsto the right output rail to maintain the large photocurrents generatedat the detectors themselves. Differential receiver 96 includes adifferential trans-impedance amplifier (or other circuits forsubtracting the first photocurrent from the second photocurrent) and ananalog-to-digital converter.

The modulatable detector-based multipliers of FIG. 10A and FIG. 11perform scalar multiplications (x times m). However, some embodimentsrelate to photonic processors including modulatable detectors designedto compute matrix-matrix (e.g., matrix-vector) multiplications. Thesephotonic processors may be implemented using single-rail or dual-railarchitectures.

An example of a modulatable detector-based dual-rail photonic processoris depicted in FIG. 12A, in accordance with some embodiments. In thisimplementation, the photonic processor is configured to multiply a 2×2matrix (M) by a 2×1 input vector (X) to obtain a 2×1 output vector (Y).This processor operates in a manner similar to the multiplier describedin connection with FIG. 11 . A first light source 10 provides an inputoptical signal having power P_(in1) and a second light source 10provides an input optical signal having power P_(in2) (although the samelight source may be used in some embodiments). P_(in2) may be equal toor different from P_(in1). Each light source is followed by adifferential optical encoder 12, which operates in the manner describedin connection with the differential optical encoder of FIG. 11 . Thefirst differential optical encoder receives voltage V_(x1), which isrepresentative of numeric value x₁. This differential optical encoderencodes the received input optical signal using voltage V_(x1) togenerate a pair of encoded optical signals having powers P_(t1) andP_(b1). These optical signals are provided as inputs to a set ofmodulatable detectors 90. The top pair of modulatable detectors receivesvoltages V_(M11) and −V_(M11), which represent numeric value M₁₁. Thebottom pair of modulatable detectors receives voltages V_(M21) and−V_(M)21, which represent numeric value M₂₁. Both differential pairs ofmodulatable detectors operate in the manner described in connection withFIG. 11 . The top pair of modulatable detectors outputs photocurrentsibis and itii, and the bottom pair of modulatable detectors outputsphotocurrents i_(b21) and i_(t21). The difference between ibis and itisis proportional to both M₁₁ and the difference between Pb₁ and Pt₁, andaccordingly, is proportional to the product M₁₁x₁. Similarly, thedifference between i_(b21) and i_(t21) is proportional to both M₂₁ andthe difference between Pb₁ and Pt₁, and accordingly, is proportional tothe product M₂₁x₁.

The second differential optical encoder receives voltage V_(x1), whichis representative of numeric value x₂. This differential optical encoderencodes the received input optical signal using voltage V_(x2) togenerate a pair of encoded optical signals having powers P_(t2) andP_(b2). These optical signals are provided as inputs to a set ofmodulatable detectors 90. The top pair of modulatable detectors receivesvoltages V_(M12) and −V_(M11), which represent numeric value M₂₁. Thebottom pair of modulatable detectors receives voltages V_(M22) and−V_(M22), which represent numeric value M₂₂. The top pair of modulatabledetectors outputs photocurrents i_(b11) and i_(t11), and the bottom pairof modulatable detectors outputs photocurrents i_(b22) and i_(t22). Thedifference between i_(b12) and i_(t12) is proportional to both M₁₂ andthe difference between P_(b2) and P_(t2), and accordingly, isproportional to the product M₁₂x₂. Similarly, the difference betweeni_(b22) and i_(t22) is proportional to both M₂₂ and the differencebetween P_(b2) and P_(t2), and accordingly, is proportional to theproduct M₂₂x₂.

The outputs of the photodetectors are combined (see, e.g., node 62),thereby allowing the photocurrents to be added to one another. Receivers96 receive the photocurrents produced by detectors 90. Receivers 96include a differential trans-impedance amplifier (or other circuits forsubtracting the first input current from the second input current) andan analog-to-digital converter. The top receiver 96 outputs numericvalue y₁=M₁₁x₁+M₁₂x₂. The bottom receiver 96 outputs numeric valuey₂=M₂₁x₁+M₂₂x₂.

An example of a 4×4 modulatable detector-based dual-rail photonicprocessor is illustrated in FIG. 12B. This processor includes four lightsources 10 (not shown), four differential encoders 12 (which encodenumeric values x₁, x₂, x₃ and x₄ into respective pairs of dual-railoptical signals), four optical splitter trees 75, thirty-two modulatabledetectors 90 (which multiply the respective inputs by M₁₁, M₂₁, M₃₁,M₄₁, M₁₂, M₂₂, M₃₂, M₄₂, M₁₃, M₂₃, M₃₃, M₄₃, M₁₄, M₂₄, M₃₄ and M₄₄), andfour receivers 96.

Although not expressly illustrated in FIGS. 11, 12A and 12B, modulatabledetectors 90 may be arranged according to the scheme depicted in FIG.9D. Accordingly, the photodetector 91 of a pair of modulatable detectorscontrol both the gain stage that is directly coupled to thephotodetector and the gain stage that is directly coupled to the otherphotodetector of the pair.

FIG. 12C illustrates an alternative optical splitter tree that does notinclude optical waveguide crossings 77. As in the tree of FIG. 12A, eachdifferential optical encoder feeds four modulatable detectors. In thetree of FIG. 12A, these four modulatable detectors 90 are all orientedin the same direction. To the contrary, in the tree of FIG. 12C, half ofthe modulatable detectors 90 are oriented in one direction and half ofthe modulatable detectors 90 are oriented in another direction (e.g.,the opposite direction). The arrangement with modulatable detectorsoriented in opposite directions is shown in the inset of FIG. 12C.Having sets of modulatable detectors oriented in different directionsallows for optical splitter trees that omit waveguide crossings, and asa result, reduces optical loss.

It should be noted that the photonic processors described in connectionwith FIGS. 12A-12B have relatively short optical paths, especially ifcompared to the photonic processors of FIGS. 6 and 7A. Compare forexample the photonic processor of FIG. 12A with the photonic processorof FIG. 6 . In the photonic processor of FIG. 12A, the optical pathsextend only from the light sources to the modulatable detectors. Bycontrast, the photonic processor of FIG. 6 has longer optical pathswhich encompass, in addition to the optical paths of FIG. 12A, thedifferential optical amplifiers.

Despite the shorter optical paths, the photonic processor of FIG. 12Atakes substantial advantage of the physical nature of optical signalprocessing. The inventors have appreciated that analog accelerators thatare implemented to operate entirely in the electrical domain suffer fromunwanted coupling between the different stages of the accelerator. Inanalog electronic accelerators, in addition to the forward electricalpath, there is an unwanted backward path that couples electrical signalsin the backward direction. This results in a variety of negativeeffects, including noise increase and speed decrease. By contrast,optical signals by nature travel only in one direction, the forwarddirection. Accordingly, there are generally no optical signals travelingin the backward direction which may otherwise negatively affect theperformance of the photonic processor (although there may be opticalback-reflections in some embodiments, the extent of these reflectionscan be reduced substantially using proper optical terminations). Theinventors have appreciated that encoding numeric values in the opticaldomain as for example shown in FIG. 12A effectively isolates the encoderfrom the multiplier, thereby avoiding the negative effects that exist infully-electrical accelerators.

V. Examples of Modulatable Detectors

As discussed above, modulatable detectors of the types described hereinare optical detectors having at least one characteristic that can becontrolled by a user using one or more electric control signals.Therefore, modulatable detectors have at least one electrical controlterminal. These detectors are designed so that application of a controlsignal (e.g., a voltage, current or charge) alters a characteristic ofthe detector, such as the detector's responsivity, gain, impedance, etc.The result is that the detector's photocurrent depends not only on theoptical power incident on the detector, but also on the control signalapplied to the detector.

As discussed above in connection with FIG. 9C-9D, in some embodiments,modulating a characteristic of a modulatable detector may involvemodulating the responsivity of one or more photodetectors 91. FIG. 13illustrates an example of a photodetector 91, in accordance with someembodiments. This photodetector is configured to operate as aphotoconductor—incident light produces electron-hole pairs which causecurrent to flow under the presence of an electric field. Thephotoconductor includes an optical waveguide 1300 (e.g., a siliconwaveguide), a photo-absorption region 1302 including germanium (thoughabsorbing materials other than germanium may be used in someembodiments), and electrodes 1304 and 1306. Optical waveguide 1300provides light to germanium region 1302. Assuming that the wavelength isbelow the germanium's absorption cut-off wavelength (about 1.9 μm insome embodiments), the incident light is absorbed by the germanium andelectron-hole pairs are generated. If a voltage is applied betweenelectrodes 1304 and 1306, an electric field is established that sweepsthe photogenerated carriers out of the germanium region, thereby givingrise to a photocurrent. In this implementation, the modulatablecharacteristic is the photoconductor's responsivity. The inventors haveappreciated, in fact, that the responsivity R (measured in amperes perwatts) of this photoconductor depends on the voltage V applied to theelectrodes. In particular, the responsivity is given by the followingexpression:

$R = {\frac{q}{hv}\frac{\tau_{n}\mu_{n}V}{w^{2}}{\eta_{i}\left( {1 - e^{{- \alpha}l}} \right)}}$

where τ_(n) is the electron recombination time, μ_(n) the electronmobility, w is the device electrode spacing, η_(i) the intrinsic quantumefficiency, α is the absorption coefficient of the detector material, vis the frequency of the incident light and l is the device depth in thelongitudinal direction with respect to the light propagation direction.It should be noted that, because the responsivity R is proportional tovoltage V, the photocurrent is also proportional to V. Therefore, thephotocurrent can be controlled by varying V.

FIGS. 14A-14B illustrate another example of a photodetector 91, inaccordance with some embodiments. FIG. 14A is a top view and FIG. 14B isa cross sectional view taken along the BB line of FIG. 14A. Thisphotodetector includes a waveguide 100 (e.g., a silicon or siliconnitride waveguide), a highly doped n region (n+ region) 102, anintrinsic region (i region) 103, a p region 104, an oxide layer (e.g.,silicon dioxide) 105, a poly-silicon layer (or a layer made of anotherconductive material) 106, an intrinsic region (i region) 107, aphoto-absorption region 108 including germanium (or including anotherabsorbing material) and a highly doped p region (p+ region) 110. In someembodiments, the germanium region is also shaped to form an opticalwaveguide.

Waveguide 100 abuts against germanium region 108. In this way, lighttraveling down waveguide 100 is transmitted to germanium region 108, andas a result, is absorbed. Germanium region 108 is positioned on top ofintrinsic region 107. For example, germanium region 108 is grownepitaxially on silicon. The highly doped regions 102 and 110 areconnected to respective electrodes. P region 104 is positioned adjacentto germanium region 108. Oxide layer 105 is positioned on top of pregion 104, and poly-silicon layer 106 is positioned on top of oxidelayer 105.

Collectively, p region 104, oxide layer 105 and poly-silicon layer 106form a metal-oxide-semiconductor capacitor (MOS cap). It should beappreciated that control capacitors other than the MOS cap may be usedin some embodiments, including for example a Shottky junction-capacitoror a graphene-based capacitor. FIG. 14C illustrates the energy banddiagram of the photodetector of FIG. 14B along the CC line. The diagramillustrates four bands. The top bands represent the conduction band whena low bias voltage is applied to the MOS cap and the conduction bandwhen a large bias voltage is applied to the MOS cap. The bottom bandsrepresent the valance band when a low bias voltage is applied to the MOScap and the valence band when of large a bias voltage is applied to theMOS cap.

The voltage applied between the n+ and p+ regions controls the electricfield along the x-axis. In the diagram of FIG. 14C, this voltageproduces a reverse bias. The reverse bias, in turn, produces an electricfield oriented along the x-axis. This electric field sweepsphotogenerated carriers away from the germanium region, assuming thatthe photocarriers have sufficient energy to overcome the energy barrierexisting at the interface between the Ge region 108 and the p region104.

The voltage applied to the MOS cap or other control capacitors (referredto as the gate voltage) determines the extent of the electron and holeenergy barriers at the interface between the Ge region 108 and the pregion 104. When the bias voltage applied to the MOS cap is low, boththe electron and the hole energy barriers are relatively large. Underthese conditions, carriers photogenerated in the germanium region areblocked, and as a result, do not produce a significant photocurrent. Tothe contrary, when the bias voltage applied to the MOS cap is large,both the electron and the hole energy barriers are relatively low. Underthese conditions, carriers photogenerated in the germanium region havesufficient energy to overcome the respective barriers, and as a result,produce a photocurrent. Thus, the voltage applied to the MOS capcontrols the responsivity of the photodetector.

In some embodiments, a photodetector includes an avalanche region inwhich photogenerated carriers experience impact ionization, therebyproducing gain. In the example of FIGS. 14A-14B, i region 103 forms anavalanche region. In other embodiments, the avalanche region may includea quasi-i region (e.g., a region with doping concentration less than10⁻¹⁴ cm⁻ 3). Impact ionization occurs in the avalanche region, whichamplifies the photocurrent. Thus, the presence of the avalanche regionincreases the sensitivity of the photodetector. In some embodiments, theresponsivity of the photodetector may be modulated by controlling thegain associated with the avalanche region.

FIG. 15A is a plot illustrating the responsivity of a photodetector ofthe type depicted in FIGS. 14A-14B. In this example, the germaniumregion has a width (measured in the direction parallel to the x-axis) of500 nm. As shown, varying the voltage applied to the MOS cap (the gatevoltage) results in a change in the responsivity of the photodetector.As discussed above, this change in responsivity occurs because thevoltage controls the extent of the energy barriers.

FIG. 15B is another plot illustrating the responsivity of aphotodetector of the type depicted in FIGS. 14A-14B. Again, the width ofthe germanium region is 500 nm. In this case, the power of the inputoptical signal is also varied. As shown, varying the input power alsocauses a change in the responsivity, which is undesirable because itnegatively effects the linearity of the photodetector. FIGS. 15C and 15Dillustrate similar plots. In the plot of FIG. 15C, the width of thegermanium region is 1000 nm. In the plot of FIG. 15D, the width of thegermanium region is 1500 nm. These plots illustrate that theresponsivity's dependence upon the input power can be mitigated byproperly selecting the width of the germanium region.

FIG. 15E further illustrates that the responsivity exhibits a weaktemperature-dependence. As for the power-dependence, thetemperature-dependence may be mitigated by properly selecting the widthof the germanium region.

The inventors have appreciated that the speed of the photodetector ofFIGS. 14A-14B depends upon the gate voltage applied to the MOS cap. Whenthe gate voltage is high enough to drive the MOS cap into inversion, thephotogenerated carriers are quickly swept away from the germaniumregion. When no gate voltage is applied, the photogenerated carriers arestored in germanium region due to the presence of the energy barrier,and largely decay by carrier recombination processes.

FIG. 16A shows the photocarrier concentration as a function of time fora temporally narrow incident optical pulse. As shown, there are two timeconstants associated with the photocarriers: one associated with therise time (Ty) and another associated with the fall time (′rR). The risetime is associated with the creation of photogenerated carriers. Thefall time, in the absence of a photocarrier sweeping field, isassociated with carrier recombination processes (which are typically onthe order of nanoseconds in imperfect semiconductors). This can besignificantly sped up by introducing a “sweeping field”. The sweepingfield can be applied periodically to remove photogenerated carriers andeffectively increase the bandwidth of the device as shown in FIG. 16B.One possible implementation of the sweeping field would be to apply ahigh voltage pulse to the MOS cap.

As discussed above, the inventors have appreciated that thephotodetector may be designed to exhibit avalanche multiplication whenan avalanche region is included between the p region 104 and the n+region 102, as shown in FIG. 14B. FIG. 17 depicts the I-Vcharacteristics in reverse bias of a representative photodetector withvarying gate voltage. As shown, avalanche multiplication kicks in ataround 10 V in this example.

As discussed above in connection with FIG. 9C-9D, in some embodiments,modulating a characteristic of a modulatable detector may involvemodulating the current gain of one or more gain stages 92. FIGS. 18A-18Hare circuit diagrams of various modulatable detectors having gain stagescharacterized by modulatable current gains, in accordance with someembodiments. In these modulatable detectors, gain stage 92 isimplemented using transistors. Further, in these modulatable detectors,optical power P_(x) (and optionally, voltage −P_(x)) is encoded withnumeric value x; voltage V_(m) (and optionally, voltage −V_(m)) isencoded with numeric value m and modulates the current gain; andphotocurrent i_(xm) (and optionally, current −i_(xm)) represents theproduct of numeric value x times numeric value m. It should beappreciated that, while these figures illustrate gain stages formedusing MOS transistors, any other suitable type of transistor may beused, including bipolar junction transistors (BJTs) and junction fieldeffect transistors (JFETs). Thus, as used herein, the term “gate”indicates the gate of a field effect transistor or the base of a bipolartransistor, the term “source” indicates the source of a field effecttransistor or the emitter of a bipolar transistor and the term “drain”indicates the drain of a field effect transistor or the collector of abipolar transistor. It should also be noted that the drain and source ofa transistor may be interchangeable. Accordingly, in some embodiments,when the drain of a transistor is described as being coupled to acertain terminal, this includes the configuration in which the source ofthe transistor is coupled to the terminal (and vice versa).

The modulatable detectors of FIGS. 18A-18H allow for encoding of signednumeric values. In these embodiments, in fact, the sign of a numericvalue (positive or negative) is represented based on the direction ofthe photocurrent(s).

The modulatable detector of FIG. 18A includes a photodetector 91 and atransistor T1 serving as gain stage 92. Photodetector 91 detects anoptical signal P_(x). The source of transistor T1 is coupled tophotodetector 91. The gate of transistor T1 receives a voltage V_(m).Voltage V_(m) controls transistor T1's gate-source voltage, and as aresult, the current gain provided by the transistor. Photocurrent i_(xm)is proportional to both numeric value x and numeric value m, therebyrepresenting the product of these numeric values. The inventors haveappreciated that such a single-ended/unbalanced circuit has threelimitations. First, this single-ended circuit is susceptible tocommon-mode and power-supply noise, both of which degrade theperformance of the modulatable detector. Second, a low magnitude voltageV_(m) turns off transistor T1, thus severely limiting the transistor'sspeed. Third, blocking of some or all the photocurrent results in chargebuildup that is dependent on optical power, resulting in an effectiveresponsivity that is dependent not only on the applied voltage V_(m) butalso on the input optical power.

FIG. 18B illustrates another modulatable detector, in accordance withsome embodiments. This modulatable detector includes two photodetectors91 to provide balanced detection of the differential optical inputsignal P_(x) with enhanced common-mode rejection ratio (CMRR) on theP_(x) inputs. The gain stage 92 includes a complementary MOS (CMOS)inverter—a p-type (PMOS) transistor T2 and an n-type (NMOS) transistorT3 enable modulation via a single-ended voltage V_(m). The photocurrent2 i _(xm) represents the product of numeric value x times numeric valuem. However, the inventors have appreciated that this modulatabledetector suffers from poor CMRR on the V_(m) input. For the circuit tooperate properly, the PMOS and NMOS transistors need to be sizedproperly to provide equal drive strength. Any process variation betweenthe PMOS and NMOS transistors results in systematic offset error,thereby negatively affecting the circuit's ability to provide equaldrive strength. Further, this modulatable detector suffers from thesecond and third problems described above in connection with themodulatable detector of FIG. 18A.

FIG. 18C illustrates another modulatable detector, in accordance withsome embodiments. This embodiment involves balanced detection (seedetectors 91) and single-ended modulation (see transistor T4, whichserves as gain stage 92). The photocurrent 2 i _(xm) represents theproduct of numeric value x times numeric value m. However, the inventorshave appreciated that this modulatable detector suffers from the samedrawbacks described above in connection with the modulatable detector ofFIG. 18B.

FIG. 18D illustrates another modulatable detector, in accordance withsome embodiments. This modulatable detector includes a gain stage withtwo transistors (T5 and T6) arranged in a differential pairconfiguration to provide differential modulation. The inventors haveappreciated that this configuration leads to a large CMRR on the V_(m)input. Further, this modulatable detector circumvents the speedlimitation described in connection with FIGS. 18A-18C. Due to thedifferential nature of the modulating electrical input signal V_(m), atleast one of the transistors is always turned on, thus enabling highspeed operation. In addition, because a current flows continuouslythrough the gain stage, the optical power-dependent charge buildup isnegligible. As a result, the overall responsivity of the modulatabledetector does not depend on the optical power. However, the inventorshave appreciated that this modulatable detector suffers from low CMRR onthe P_(x) input.

The modulatable detectors of FIGS. 18E-18H provide fully differentialmodulation and balanced detection and address the problems described inconnection with FIGS. 18A-18D. FIG. 18E illustrates another modulatabledetector, in accordance with some embodiments. This modulatable detectorincludes a gain stage with two differential pairs (see transistor pairT7-T8 and transistor pair T9-T10) with cross-coupled connections. Thedrain of transistor T7 is coupled to the drain of transistor T9, and thedrain of transistor T8 is coupled to the drain of transistor T10.Photodetectors 91 are coupled to the sources of transistors T7-T10.Voltages V_(m) and −V_(m) control the current gain of the gain stage,and photocurrents 2 i _(xm) and −2 i _(xm) represent the product ofnumeric value x times numeric value m. The modulatable detector of FIG.18E provides high speed operation, optical-power-independent overallresponsivity, robustness to process variation and mismatch, and largeCMRR on both P_(x) and V_(m) inputs.

FIG. 18F illustrates another modulatable detector, in accordance withsome embodiments. This modulatable detector is similar to themodulatable detector of FIG. 18E. However, this modulatable detectorincludes a gain stage having CMOS inverters with differential pairs oftransistors. PMOS transistor T11 and NMOS transistor T12 have drainsthat are coupled to one another. Similarly, PMOS transistor T13 and NMOStransistor T14 have drains that are coupled to one another. Onephotodetector 91 is coupled to the sources of transistors T12 and T14.One photodetector 91 is coupled to the sources of transistors T11 andT13. This modulatable detector can be viewed as the differential versionof the modulatable detector of FIG. 18B.

FIG. 18G illustrates another modulatable detector, in accordance withsome embodiments. This modulatable detector is similar to themodulatable detector of FIG. 18E, but it includes a gain stage with onedifferential pair of transistors T15-T16. This modulatable detectorincludes a node N1, which is coupled to both photodetectors 91 and tothe sources of transistors T15 and T16. This modulatable detector can beviewed as the fully differential version of the modulatable detector ofFIG. 18C.

FIG. 18H illustrates another modulatable detector, in accordance withsome embodiments. This modulatable detector includes a gain stage withtwo CMOS transmission gates. The drains of transistors T17 and T18 arecoupled to each other and the sources of transistors T17 and T18 arealso coupled to each other. Similarly, the drains of transistors T19 andT20 are coupled to each other and the sources of transistors T19 and T20are also coupled to each other. NMOS transistor T17 and PMOS transistorT18 form a first complementary transmission gate. NMOS transistor T20and PMOS transistor T19 form a second complementary transmission gate.Node N2 is coupled to both complementary transmission gates and to bothphotodetectors 91.

FIG. 19A illustrates the steady-state overall responsivity (measured interms of photocurrent 2 i _(xm) and input power P_(x)) for themodulatable detector FIG. 18E plotted as a function of voltage V_(m).The other modulatable detectors have similar responses. This plotsreflects the fact that voltage V_(m) modulates the current gain providedcollectively by transistors T7-T10. It should be noted that the overallresponsivity is nearly independent of the input optical power. FIG. 19Billustrates the transient overall responsivity as a function of time.The transient response exhibits a settling time of less than 500 ps,thus indicating high-speed operation in the gigahertz range.

Photonic processors of the types described herein may include tens ifnot hundreds of thousands of modulatable detectors. For example, aphotonic processor configured to perform multiplications on 256×256matrices may include, in some embodiments, as many as 131,072modulatable detectors. The inventors have appreciated that it would bedesirable to integrate the photonic processor on a single chip in orderto reduce manufacturing costs, increase speed of operation and limitpower consumption. Because the photonic processors of the typesdescribed herein include both photonic and electronic circuits,integrating a photonic processor on a single chip involveselectronic-photonic co-integration. This may be achieved at least in twoways.

The first way involves forming transistors and silicon photonics on thesame silicon substrate. For example, silicon photonics and transistorsmay be formed on the same silicon layer. A representative arrangement isdepicted in FIG. 20A, in accordance with some embodiments. In this case,both the transistors and the silicon photonics are formed on substate300 (e.g., a silicon bulk substrate or a silicon-on-insulatorsubstrate). A cladding 302 (e.g., silicon dioxide layer) is formedbetween the substrate's handle and silicon layer 304. Transistors 306(which include, among others, the transistors used in any of thearrangements of FIGS. 18A-18H and, optionally, the transistors thatconstitute controller 17) are patterned on silicon layer 304. Similarly,silicon photonics 308 (which include, among others, the opticalencoders, optical multipliers, splitter trees described above) are alsopatterned on silicon layer 304. Germanium region 310 (which may be usedto form any of the photodetectors described above) is formed on top ofsilicon layer 304, for example via epitaxial growth.

The second way involves forming the silicon photonics and thetransistors on separate substrates and bonding the substrates together.A representative arrangement is depicted in FIG. 20B, in accordance withsome embodiments. Here, transistors 306 are formed on substrate 300 andsilicon photonics 308 on substrate 400. As in the previous example,silicon photonics 308 are formed on a silicon layer (404), and germaniumregion 310 is formed on top of silicon layer 404. Substrates 300 and 400are bonded to one another using flip-chip bonding techniques. Forexample, the substrates may be placed in electrical communication usingthrough-oxide vias (as shown in FIG. 20B) passing through cladding 414and/or using through-silicon vias (not shown in FIG. 20B).

VI. Conclusion

Having thus described several aspects and embodiments of the technologyof this application, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those of ordinaryskill in the art. Such alterations, modifications, and improvements areintended to be within the spirit and scope of the technology describedin the application. It is, therefore, to be understood that theforegoing embodiments are presented by way of example only and that,within the scope of the appended claims and equivalents thereto,inventive embodiments may be practiced otherwise than as specificallydescribed. In addition, any combination of two or more features,systems, articles, materials, and/or methods described herein, if suchfeatures, systems, articles, materials, and/or methods are not mutuallyinconsistent, is included within the scope of the present disclosure.

Also, as described, some aspects may be embodied as one or more methods.The acts performed as part of the method may be ordered in any suitableway. Accordingly, embodiments may be constructed in which acts areperformed in an order different than illustrated, which may includeperforming some acts simultaneously, even though shown as sequentialacts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified.

The terms “approximately” and “about” may be used to mean within ±20% ofa target value in some embodiments, within ±10% of a target value insome embodiments, within ±5% of a target value in some embodiments, andyet within ±2% of a target value in some embodiments. The terms“approximately” and “about” may include the target value.

What is claimed is:
 1. (canceled)
 2. A photonic device configured toperform a mathematical operation comprising: an optical encoder; amodulatable detector coupled to an output of the optical encoder, themodulatable detector comprising a first photodetector and a firsttransistor; and a controller coupled to both the optical encoder and themodulatable detector, the controller being configured to: obtain a firstnumeric value and a second numeric value, control the optical encoder togenerate an encoded optical signal by modifying an input optical signalusing the first numeric value, control the first transistor using thesecond numeric value to generate a photocurrent in response to the firstphotodetector receiving the encoded optical signal, and obtain a resultof the mathematical operation using the photocurrent.
 3. The photonicdevice of claim 2, wherein controlling the first transistor using thesecond numeric value to generate a photocurrent comprises applying, to agate of the first transistor, a voltage that is encoded with the secondnumeric value.
 4. The photonic device of claim 2, wherein themodulatable detector further comprises: a second photodetector and asecond transistor, wherein the first and second photodetectors areconfigured to provide balanced detection, and the first and secondtransistors form a first inverter.
 5. The photonic device of claim 4,wherein the modulatable detector further comprises: a third transistorand a fourth transistor forming a second inverter, wherein the firstinverter and the second inverter are in parallel to each other.
 6. Thephotonic device of claim 5, wherein the controller is further configuredto control the second, third and fourth transistors using the secondnumeric value.
 7. The photonic device of claim 2, wherein themodulatable detector further comprises: a second photodetector, whereinthe first and second photodetectors are configured to provide balanceddetection; and a node coupled to the first transistor and both the firstand second photodetectors.
 8. The photonic device of claim 7, whereinthe modulatable detector further comprises: a second transistor, whereinthe node is further coupled to the second transistor.
 9. The photonicdevice of claim 8, wherein the controller is further configured tocontrol the second transistor using the second numeric value.
 10. Thephotonic device of claim 2, wherein the modulatable detector furthercomprises: a second transistor, wherein the first and second transistorsform a first differential pair.
 11. The photonic device of claim 10,wherein the modulatable detector further comprises: a secondphotodetector; and third and fourth transistors forming a seconddifferential pair, wherein the first photodetector is coupled to thefirst differential pair and the second photodetector is coupled to thesecond differential pair.
 12. The photonic device of claim 11, whereinthe first and second differential pairs have cross-coupled connections.13. The photonic device of claim 11, wherein the controller is furtherconfigured to control the second, third and fourth transistors using thesecond numeric value.
 14. The photonic device of claim 2, wherein themodulatable detector further comprises: a second photodetector; second,third and fourth transistors, wherein the first and second transistorsform a first transmission gate and the third and fourth transistors forma second transmission gate; and a node coupled to both the first andsecond photodetectors and both the first and second transmission gates.15. The photonic device of claim 14, wherein the controller is furtherconfigured to control the second, third and fourth transistors using thesecond numeric value.
 16. The photonic device of claim 2, whereinobtaining the result of the mathematical operation comprises obtaining aproduct of the first numeric value times the second numeric value.
 17. Aphotonic device configured to perform a mathematical operationcomprising: an optical encoder; a modulatable detector coupled to anoutput of the optical encoder, the modulatable detector comprising abalanced detection unit and a differential modulation unit; and acontroller coupled to both the optical encoder and the modulatabledetector, the controller being configured to: obtain a first numericvalue and a second numeric value, control the optical encoder togenerate an encoded optical signal by modifying an input optical signalusing the first numeric value, control the differential modulation unitusing the second numeric value to generate a pair of photocurrents inresponse to the balanced detection unit receiving the encoded opticalsignal, and obtain a result of the mathematical operation using the pairof photocurrents.
 18. The photonic device of claim 17, wherein obtainingthe result of the mathematical operation comprises obtaining a productof the first numeric value times the second numeric value.
 19. Thephotonic device of claim 17, wherein controlling the differentialmodulation unit using the second numeric value to generate a pair ofphotocurrents comprises applying, to gates of the differentialmodulation unit, voltages encoded with the second numeric value.
 20. Thephotonic device of claim 17, wherein: the differential modulation unitcomprises first and second transistors forming a first differential pairand third and fourth transistors forming a second differential pair,wherein the first and second differential pairs have cross-coupledconnections.
 21. The photonic device of claim 17, wherein: thedifferential modulation unit comprises first and second transistorsforming a first inverter and third and fourth transistors forming asecond inverter, wherein the first inverter and the second inverter arein parallel to each other.
 22. The photonic device of claim 17, wherein:the differential modulation unit comprises first and second transistorsand the balanced detection unit comprises first and secondphotodetectors, and the modulatable detector further comprises a nodecoupled to both the first and second transistors and both the first andsecond photodetectors.
 23. The photonic device of claim 17, wherein: thedifferential modulation unit comprises first, second, third and fourthtransistors, wherein the first and second transistors form a firsttransmission gate and the third and fourth transistors form a secondtransmission gate.